Modelo computacional de la interacción Phytophthora ... · VIII Modelo computacional de la...

Modelo computacional de la interacción

compatible entre Phytophthora infestans y

Solanum tuberosum a través de la

reconstrucción computacional del

metabolismo de la

planta y datos de expresión génica

Kelly Johana Botero Orozco

Universidad Nacional de Colombia

Facultad de Ingeniería, Departamento de Ingeniería de Sistemas e Industrial

Bogotá, Colombia

2016

Modelo computacional de la interacción

compatible entre Phytophthora infestans y

Solanum tuberosum a través de la

reconstrucción computacional del

metabolismo de la

planta y datos de expresión génica

Kelly Johana Botero Orozco

Tesis presentada como requisito parcial para optar al título de:

Magister en Bioinformática

Director:

Ph.D. Andres Mauricio Pinzón Velasco

Línea de Investigación:

Biología de Sistemas - Reconstrucción y Análisis de Redes Biológicas

Grupos de Investigación:

Bioinformática y Biología de Sistemas - Universidad Nacional de Colombia

Universidad Nacional de Colombia

Facultad de Ingeniería, Departamento de Ingeniería de Sistemas e Industrial

Bogotá, Colombia

2016

Agradecimientos

Al profesor Andres Mauricio Pinzón, por su asesoría y apoyo durante el desarrollo de este trabajo.

A mi familia, por ser el gran motor de mi vida, y por todos los años de amor y enseñanzas, que han

hecho de mí, una mujer que lucha con pasión por alcanzar sus metas.

A mi compañero de vida, por ser la persona que alegra cada uno de mis días y por darme su apoyo

incondicional.

A Daniel Camilo Osorio, porque fue un excelente compañero de estudio.

Al grupo de investigación en bioinformática y biología de sistemas por acogerme y permitirme

compartir diversas experiencias académicas y de vida.

Al grupo de micología y fitopatología de la Universidad de los Andes por los aportes a este trabajo.

A la profesora Liliana López Kleine por su asesoría para integrar a los flujos de reacción datos de

expresión ausentes.

Al profesor Pedro Adolfo Jiménez por las sugerencias para incorporar las reacciones lumínicas de la

fotosíntesis a la reconstrucción metabólica a escala genómica de papa.

Resumen y Abstract VII

Resumen

Solanum tuberosum, la papa común, es uno de los principales cultivos para el consumo

humano; el patógeno más importante que afecta su producción es el oomicete Phytophthora

infestans, causante de la enfermedad del tizón tardío. Análisis de la expresión génica en

plantas enfermas sugieren disminución de la capacidad de fijación de CO2. Este trabajo

presenta un modelo metabólico computacional de la interacción compatible entre S.

tuberosum y P. infestans, para analizar a nivel sistémico, los mecanismos metabólicos

asociados a la fotosíntesis (reacciones lumínicas y fijación de CO2) en plantas enfermas.

Para este fin se reconstruyó la red metabólica de la planta a partir de anotaciones funcionales

del genoma de S. tuberosum y bases de datos bioquímicas y metabólicas. La reconstrucción

fue refinada manualmente y automáticamente usando el paquete “g2f”, desarrollado para

este trabajo en el lenguaje de programación R. La reconstrucción refinada se transformó en

un modelo metabólico computacional, al cual se le integraron datos de expresión génica

obtenidos durante la interacción compatible entre S. tuberosum y P. infestans en tres

momentos (0, 2 y 3 días post-inoculación); para esto se desarrolló el paquete de R

“exp2flux”, que permite integrar restricciones de flujo a partir de datos ómicos a modelos

metabólicos. El análisis de balance de flujo, mostró disminución de flujos metabólicos en

la ruta de fijación de CO2 y en las reacciones lumínicas de la fotosíntesis durante la

infección. Este trabajo reafirma la disminución de la capacidad de fijación de CO2 y sugiere,

además, una supresión general de la capacidad fotosintética en la planta durante la

interacción compatible con P. infestans, probablemente asociada a un mecanismo de

defensa. Aquí se reporta la primer reconstrucción metabólica a escala genómica de S.

tuberosum y el primer modelo metabólico a escala genómica de una interacción planta-

patógeno.

Palabras clave: Solanum tuberosum, Phytophthora infestans, interacción planta patógeno,

modelo metabólico a escala genómica, fotosíntesis.

VIII Modelo computacional de la interacción compatible entre Phytophthora infestans y

Solanum tuberosum

Abstract

The potato plant (Solanum tuberosum) is one of the main crops for human consumption; the

most important pathogen that affects its production is the oomycete Phytophthora infestans,

which causes late blight disease. Gene expression analysis suggests decreased CO2 fixation

capacity in diseased plants. This work presents a computational metabolic model of the

compatible interaction between S. tuberosum and P. infestans which allowed us to study the

metabolic mechanisms associated with photosynthesis (light reactions and CO2 fixation) at

a systemic level in diseased plants. For this purpose, the reconstruction of the metabolic

network of the plant was obtained from functional annotations of the S. tuberosum genome

and biochemical and metabolic databases. The reconstruction was refined manually and

automatically using the R package "g2f", developed for this work. Refined reconstruction

was transformed into a computational metabolic model, and gene expression data during

the compatible interaction between S. tuberosum and P. infestans at three times (0, 2 and 3

days post-inoculation) was integrated into the model. For this, the "exp2flux" R package

was developed, which allows the integration of flux constraints from omics data to

metabolic models. Flux balance analysis showed decreased metabolic fluxes in the CO2

fixation pathway and in the light reactions of the photosynthesis during infection. This work

reaffirms the decrease of the CO2 fixation capacity and also suggests a general suppression

of the photosynthetic capacity in the plant during the interaction compatible with P.

infestans, likely associated to an oxidative defense mechanism. Here, the first genome-scale

metabolic reconstruction of S. tuberosum and the first genome-scale metabolic model of a

plant-pathogen interaction are reported.

Keywords: Solanum tuberosum, Phytophthora infestans, plant-pathogen interaction,

genome-scale metabolic model, photosynthesis.

Contenido IX

Contenido

Pág.

Resumen ......................................................................................................................... VII

Lista de figuras ................................................................................................................ XI

Lista de tablas ................................................................................................................. XII

Objetivos ....................................................................................................................... XIII Objetivo general ....................................................................................................... XIII Objetivo específicos .................................................................................................. XIII

Introducción ...................................................................................................................... 1 Generalidades de la interacción entre Phytophthora infestans y Solanum tuberosum ............. 1 Relevancia de la enfermedad de tizón tardío de la papa...................................................... 1 Estudios moleculares sobre la interacción entre S. tuberosum y P.infestans .......................... 2 Biología de sistemas: una aproximación para la compresión de sistemas complejos .............. 3 Reconstrucciones metabólicas a escala genómica .............................................................. 4 Generación del modelo metabólico de la interacción entre S. tuberosum y P. infestans .......... 6

1. A Genome-Scale Metabolic Model of Potato suggests a mechanism of photosynthetic suppression during the compatible interaction with Phytophthora

infestans 9 Abstract: ...................................................................................................................... 9 1.1 Introduction ..................................................................................................... 10 1.2 Results and discussion ...................................................................................... 13

1.2.1 Metabolic reconstruction ........................................................................ 13 1.2.2 General model properties ........................................................................ 14 1.2.3 Metabolic phenotype analysis of the compatible interaction between S.

tuberosum and P. infestans .................................................................................... 15 1.2.4 Photosynthesis and carbon fixation metabolism ......................................... 16

1.3 Conclusions ..................................................................................................... 23 1.4 Materials and Methods ...................................................................................... 23

1.4.1 Metabolic reconstruction. ....................................................................... 23 1.4.2 Metabolic reconstruction refinement ........................................................ 23 1.4.3 Transformation of the reconstructed network into a genome-scale metabolic

model 26 1.4.4 Incorporation of gene expression data into the genome-scale metabolic

model 27 1.4.5 Metabolic flux model optimization .......................................................... 27

1.5 Supplementary ................................................................................................. 29

X Modelo computacional de la interacción compatible entre Phytophthora infestans y

Solanum tuberosum

2. Finding and filling gaps in metabolic networks through the ‘g2f’ R package ... 31 Abstract .................................................................................................................... 31 2.1 Introduction .................................................................................................... 31 2.2 Installation and functions .................................................................................. 34

2.2.1 Downloading a reference from the KEGG database ................................... 34 2.2.2 Calculating the addition cost ................................................................... 34 2.2.3 Performing a gap find and fill ................................................................. 35 2.2.4 Identifying blocked reactions .................................................................. 36

2.3 Summary ........................................................................................................ 36

3. Constraining the metabolic reconstruction: Incorporating expression data as FBA limits through the ‘exp2flux’ R package .............................................................. 39

Abstract .................................................................................................................... 39 3.1 Introduction .................................................................................................... 39 3.2 Installation and functions .................................................................................. 42

3.2.1 Inputs .................................................................................................. 42 3.2.2 Converting gene expression data to FBA limits ......................................... 42 3.2.3 Identifying flux changes between scenarios .............................................. 45

3.3 Summary ........................................................................................................ 46

Bibliografía ..................................................................................................................... 47

Contenido XI

Lista de figuras

Pág.

Figure 0-1: Reportes de redes metabólicas a escala genómica en plantas ................................... 6

Figure 1-1: Required enzymatic activities to catalyze the reactions in the model. ..................... 15

Figure 1-2: Metabolic fluxes of the biomass synthesis and noncyclic photophosphorylation

reactions during compatible interaction between S. tuberosum and P. infestans. The flux reaction

of biomass synthesis and noncyclic photophosphorylation decrease at 1 dpi and 3dpi. ............... 16

Figure 1-3: Metabolic flux distribution patterns of the fixation carbon pathway and some reactions

associated with photorespiration and carbohydrate synthesis. (a) Metabolic flux distribution

patterns for 0dpi; (b) metabolic flux distribution patterns for 1 dpi; and (c) metabolic flux

distribution patterns for 3 dpi. ............................................................................................. 19

Figure 1-4: Metabolic fluxes of GAP formation and starch synthesis. The fluxes of these reactions

showed the same trend through infection time. ..................................................................... 22

Figure 1-5: General scheme of the refinement of potato metabolic network. The lines indicate the

trajectory from data sources to the refined metabolic network. ................................................ 24

Figure 3-1: Workflow to integrate omics data into reaction flux of a genome-scale metabolic

model. ............................................................................................................................. 41

Figure 3-2: Flux differences between an unconstrained and a constrained model. Constraints were

calculated through the exp2flux R package using simulated gene expression data. .................... 44

Contenido XII

Lista de tablas

Pág.

Table1-1. Summary of the manual and semi-automatic refinement connectivity reconstruction .. 14

Supplementary Table 1-2: Refined pathways in the metabolic network reconstruction. We show

all the pathways included in the metabolic network of S. tuberosum. Pathway association was

assigned based in the categorization of the KEGG Pathways database. The colors correspond to the

level of curation of each pathway ........................................................................................ 29

Supplementary Table 1-3: Reaction Fluxes of the metabolic pathways of interest in S.tuberosum

to evaluate photosynthetic capacity through of compatible interaction with P. infestans. ............ 30

Contenido XIII

Objetivos

Objetivo general

Generar un modelo computacional del metabolismo de Solanum tuberosum que permita

identificar los posibles mecanismos de inhibición de su capacidad fotosintética durante la

interacción con Phytophthora infestans

Objetivo específicos

● Identificar el conjunto de reacciones bioquímicas y propiedades metabólicas de

S.tuberosum

● Obtener una representación matemática y computacional del metabolismo S.tuberosum

● Identificar los posibles mecanismos moleculares relacionados con la inhibición de la

capacidad fotosintética en S. tuberosum durante la interacción compatible con P. infestans

Introducción

Generalidades de la interacción entre Phytophthora infestans y

Solanum tuberosum

Phytophthora infestans Mont. De Bary, es un Oomycete patógeno causante de la

enfermedad del tizón tardío de la papa Solanum toberosum [1]. La propagación de la

infección por este patógeno ocurre rápidamente en el follaje y en los tubérculos causando

necrosis en la planta[2]. La infección de P. infestans en los tejidos de S. tuberosum se

desarrolla durante el ciclo de vida hemibiotrófico del patógeno[3], el cual puede resumirse

en cuatro etapas: (1) adhesión de zoosporas móviles a la superficie celular [4]; (2)

penetración del patógeno a la célula mediante la formación de estructuras especializadas

llamadas haustorios [5] y secreción de enzimas de degradación como fosfolipasas,

glucanasas y endopoligalacturonasas [6]; (3) colonización a través de la liberación de

proteínas efectoras del patógeno que manipulan procesos fisiológicos de la planta [4], [6],

[7]. En esta etapa, cuando las proteínas efectoras no son reconocidas por el sistema inmune

o cuando el patógeno genera estrategias para evadir respuestas de defensa del hospedero, la

interacción planta-patógeno (patosistema) es compatible y la planta infectada se considera

susceptible, de lo contario, la planta se considera resistente y la interacción incompatible

[8], [9]; y (4) en plantas susceptibles el patógeno adquiere nutrientes y se propaga por los

tejidos de la planta [4], [10].

Relevancia de la enfermedad de tizón tardío de la papa

La papa es el cuarto cultivo alimentario más importante (después del maíz, el arroz y el

trigo) para el consumo humano [11]. Los tubérculos de papa suministran principalmente

carbohidratos, pero también son fuente de proteínas, vitaminas, fibra dietética y minerales

2 Introducción

[12]. Históricamente, el tizón tardío o gota de la papa es el principal factor que afecta la

producción de la papa [13], [14]. Desde su primer brote de pandemia en la mitad del siglo

XIX, P. infestans ha sido el patógeno más destructivo de las plantaciones de este cultivo, lo

que resulta en pérdidas anuales que serían suficientes para alimentar a varios cientos de

millones de personas [15]. Además, el valor económico de esta pérdida y el costo de

protección del cultivo se estima en 6,7 mil millones de dólares por año [16]. A pesar de la

importancia económica y social que implica el tizón tardío de la papa, los principales

mecanismos metabólicos que subyacen la patogenicidad causada por P. infestans son aún

poco entendidos [17].

Estudios moleculares sobre la interacción entre S. tuberosum y

P.infestans

Múltiples investigaciones han intentado comprender aspectos moleculares que subyacen la

interacción compatible e incompatible entre P. infestans y S. toberosum [5], [8], [9], [18]–

[20]. Algunas han utilizado estrategias como expresión génica [17]–[22] y genómica [23],

la mayoría de estos estudios se han enfocado en identificar factores que favorecen la

interacción incompatible de las plantas resistentes a P. infestans [18], [21], [24]–[28],

identificado así, genes y compuestos involucrados en la respuesta de defensa de la planta

ante la invasión patogénica [21], [24], [25]. No obstante, también se han desarrollado

investigaciones con microarreglos basados en clones ADNc[19], análisis de transcriptoma

mediante DeepSAGE [29] y análisis de RNA-Seq [18] para intentar comprender la

interacción compatible del patosistema. Particularmente, Restrepo et al., (2005) encontraron

que 358 genes se reprimen y 241 genes se sobre expresan durante cinco puntos de tiempo

del proceso de infección, estos resultados y otros análisis complementarios con rtq-PCR

permitieron concluir que la interacción compatible suprime genes involucrados en la ruta

metabólica de fijación de CO2 y genes involucrados en la ruta metabólica del ácido

jasmonico, la cual está asociada al sistema de defensa de plantas [19].

Por otra parte, en 2011 el consorcio para la secuenciación de la papa (PGSC, del inglés

Potato Genome Sequencing Consortium) reportó la secuenciación del genoma de S.

Introducción 3

tuberosum con 39,031 genes codificantes de proteínas, entre los que se identificaron

homólogos altamente relacionados con genes de resistencia (R1, RB, R2, R3a, Rpi-blb2 and

Rpi-vnt1.1) al tizón tardío de la papa [30]. De otro lado, el genoma de P. infestans también

ha sido reportado con 17,797 genes codificantes de proteínas. La comparación de este

genoma con las especies cercanas, Phytophthora sojae y Phytophthora ramorum mostró que

el 70% de sus genes son ortólogos y permitió identificar genes que codifican proteínas

efectoras que alteran la fisiología del hospedero y favorecen la patogénesis [16].

Los estudios descritos anteriormente, representan una importante fuente de conocimiento

acerca de mecanismos y moléculas que subyacen la interacción planta-patógeno, sin

embargo, dado que la respuesta biológica de las plantas al interactuar con un patógeno está

regulada por complejas redes de interacción génica, proteica y metabólica [31], [32], estos

estudios enmarcan una visión fragmentada de los procesos de evasión o acogida del

patógeno por parte de la planta y evidencian la necesidad de contemplar la utilización de

metodologías más integrativas.

En este caso, donde datos experimentales de la interacción, así como datos genómicos de S.

tuberosum comienzan a acumularse, es factible y conveniente integrar toda esa información

dentro de un modelo metabólico in silico de la planta. Esta aproximación permite obtener

un modelo descriptivo de la interacción compatible entre P. infestans y S. tuberosum, el cual

fortalecería la capacidad predictiva de futuras respuestas de la planta, bajo diferentes

condiciones y mostraría una visión global y detallada del sistema de interacción que se lleva

a cabo en este patosistema y particularmente al interior celular del hospedero [17].

Biología de sistemas: una aproximación para la compresión de

sistemas complejos

Durante la segunda mitad del siglo XX, la biología estuvo fuertemente influenciada por

enfoques reduccionistas que buscaban generar información sobre los componentes

individuales de los sistemas biológicos, con la cual se buscaba inferir sobre las propiedades

de un organismo como un todo [33]–[35]. Este enfoque ha generado importantes logros y

4 Introducción

una enorme cantidad de datos, sin embargo, no permite la comprensión de sistemas

complejos [36], [37], como por ejemplo, la relación genotipo – fenotipo de rasgos

fenotípicos que son el resultado de múltiples interacciones de productos génicos[32], [38].

Actualmente, la compresión de procesos biológicos más complejos, como por ejemplo los

que se llevan a cabo durante el conjunto de reacciones bioquímicas que denominamos

metabolismo [39], no se centra en el estudio de componentes individuales (ej. enzimas y

metabolitos), sino en la naturaleza de los vínculos que los conectan [33]. Esta orientación,

de naturaleza más holista, es conocida como Biología de Sistemas o biología sistémica, y

busca predecir el comportamiento y entender las propiedades que emergen de los sistemas

biológicos ante estímulos y cambios en el ambiente, entendiéndolos como un conjunto de

componentes que interactúan de manera compleja a nivel de red. Estos sistemas son

susceptibles de ser modelados mediante métodos computacionales con alta capacidad

predictiva, diferenciándose así de la aproximación reduccionista que se enfoca en el estudio

de los componentes individuales de manera aislada.

Reconstrucciones metabólicas a escala genómica

El surgimiento y avance de las tecnologías secuenciación de siguiente generación, ha

permitido anotar con un alto nivel de precisión las funciones del genoma de los organismos

[40]. Estas anotaciones son fundamentales para la reconstrucción de redes metabólicas a

escala genómica (RMEG), las cuales son una representación de las reacciones bioquímicas

presentes en un organismo, que pueden ser analizadas, interpretadas y predichas, mediante

simulación computacional [33]. Un método computacional ampliamente utilizado para

generar predicciones fenotípicas de la actividad metabólica de un organismo se encuentra

en el análisis de balance de flujo (FBA, por sus siglas en inglés). EL FBA implica la

optimización lineal del conjunto de reacciones de una red metabólica en estado estacionario,

con el fin de predecir una distribución óptima de flujos metabólicos, que maximiza objetivos

metabólicos inferidos, bajo un conjunto de restricciones que limitan la solución de sistema

[41]. El establecimiento de los objetivos metabólicos supone que la célula desempeña

óptimamente una función metabólica [42]. Ejemplos de funciones objetivo incluyen, la

Introducción 5

maximización de biomasa, la producción de ATP y la producción de un metabolito de interés

[43].Una vez que se fija la función objetivo, el sistema en estado estacionario puede

resolverse para obtener una distribución de flujos óptima que permiten interpretar las

capacidades metabólicas de la red [42]. Para que la optimización obtenga una distribución

de flujos fisiológicamente viables, el espacio de solución del sistema en el FBA se debe

restringir con restricciones termodinámicas y restricciones dadas por funciones metabólicas

en condiciones particulares. Estas restricciones son impuestas a los límites de los flujos

(superior e inferior) de las reacciones en la red metabólica [44], [45].

La modelación de RMEG a través de FBA tiene importantes alcances sobre los sistemas

biológicos complejos, permite por ejemplo: (1) inferir la función de redes bioquímicas; (2)

plantear hipótesis dirigidas que pueden ser resueltas experimentalmente para la

incorporación de nuevo conocimiento biológico, y (3) descubrir propiedades emergentes de

las redes, ya que se enfoca en toda la red metabólica, más que, en genes o rutas individuales

[46].

Para plantas, hasta el 2009 solo se reportaban las RMEG de Arabidopsis thaliana [47], [48],

y de la semilla de cebada (Hordeum vulgare) [49]. Esta escasez de reconstrucciones se

justificaba en el bajo número de genomas completos disponibles; actualmente se han

secuenciado y publicado más de 100 genomas de plantas en la base de datos Genbank del

National Center for Biotechnology Information – NCBI [50], [51]. Ante este panorama, las

reconstrucciones metabólicas en plantas están creciendo con modelos disponibles para Zea

mays[52]–[54], Sorghum bicolor [52], Saccharum officinarum[52]; Brassica napus [55],

[56], Oryza sativa [57] y Solanum lycopersicum [58] (Figura 0-1).

6 Introducción

Figure 0-1: Reportes de redes metabólicas a escala genómica en plantas

A partir de estas RMEGs, múltiples análisis y predicciones metabólicas se han se llevado a

cabo. Particularmente, para recrear fenotipos metabólicos específicos de las plantas, algunos

estudios han integrado datos ómicos como restricciones de flujo de reacción en las RMEGs

[59]. Töpfer et al., (2013) incorporaron, mediante el método E-Flux [60], datos de expresión

de genes [61] a la RMEG de Arabidopsis thaliana [62] para intentar comprender funciones

metabólicas de aclimatación a diferentes temperaturas e intensidades de luz [63]. Por su

parte, Simons et al., (2014) con el propósito de profundizar en el metabolismo del nitrógeno

en la planta del maíz, incorporaron a la RMEG de Zea mays [53] datos transcriptómicos y

proteómicos de experimentos de plantas silvestres y mutantes, sometidas a condiciones

óptimas y bajas de nitrógeno. Para ello, apagaron las reacciones asociadas a transcritos y

proteínas que presentaron bajos niveles de expresión en los experimentos [54].

Generación del modelo metabólico de la interacción entre S.

tuberosum y P. infestans

Con la disponibilidad del genoma de S. tuberosum y datos de expresión génica durante la

interacción compatible, este trabajo generó un modelo computacional que representa el

metabolismo celular de la hoja de una planta enferma, con el fin de comprender los

mecanismos metabólicos que subyacen la posible disminución de la capacidad de fijación

de CO2, mencionada previamente[19]. Este trabajo pone a disposición de la comunidad

científica las bases fundamentales para la modelación de la red metabólica a escala genómica

de S.tuberosum, sobre las cuales se podrán entender otros mecanismos metabólicos de la

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Arabidopsis thaliana

Hordeum vulgare

Sorghum bicolor

Saccharum officinarum

Brassica napus

Oryza sativa

Solanum lycopersicum

Introducción 7

planta durante la interacción compatible o bajo otras condiciones ambientales, plantear

novedosas hipótesis dirigidas, orientar investigaciones para realizar ingeniería metabólica

en la planta e identificar propiedades emergentes del metabolismo de la planta, que no

podrían observarse con el estudio de moléculas y procesos individuales.

Adicionalmente, se diseñaron e implementaron el paquete “g2f” para la etapa de

refinamiento de la red metabólica y el paquete “exp2flux” para la etapa de generación del

modelo metabólico de la interacción planta-patógeno. Ambos paquetes están desarrollados

en el lenguaje de programación R y están disponibles en The Comprehensive R Archive

Network (CRAN).

En este sentido, este trabajo presenta tres capítulos en los que se exponen los principales

conceptos, métodos, desarrollos y aplicaciones necesarios para la generación del modelo

metabólico a escala genómica de la interacción compatible entre S. tuberosum y P. infestans.

En el primer capítulo titulado “A genome-Scale metabolic model of potato suggests a

mechanism of photosynthetic suppression during the compatible interaction with

Phytophthora infestans” se presenta el desarrollo de la primer red metabólica a escala

genómica de S. tuberosum y el primer modelo metabólico a escala genómica de la

interacción compatible entre la planta y P. infestans. El modelo fue evaluado principalmente

para observar las variaciones de los flujos metabólicos asociados a fotosíntesis, lo que reflejó

disminución de la capacidad fotosintética durante la infección. En el segundo capítulo

titulado “Finding and filling gaps in metabolic networks through the ‘g2f’ R package”, se

presenta el paquete “g2f”, el cual puede realizar gap find y gap fill en reconstrucciones

metabólicas a escala genómica. Este paquete fue usado para el refinamiento semiautomático

y automático de la red metabólica de la papa. En el último capítulo titulado “Constraining

the metabolic reconstruction: Incorporating expression data as FBA limits through the

‘exp2flux’ R package”, se presenta el paquete “exp2flux”, el cual permite incorporar datos

de expresión a modelos metabólicos a escala genómica. Este paquete fue usado para integrar

datos de expresión de la interacción compatible entre S. tuberosum y P. infestans a la red

metabólica de la planta. .

https://cran.r-project.org/

https://cran.r-project.org/

Capítulo 1 9

1. A Genome-Scale Metabolic Model of Potato

suggests a mechanism of photosynthetic

suppression during the compatible interaction

with Phytophthora infestans

Abstract:

Phytophthora infestans is a plant pathogen that causes an economically important plant

disease known as late blight in potato (Solanum tuberosum) plants and several other hosts.

In spite of the importance of the disease, the molecular mechanisms underlying the

compatibility between the pathogen and its hosts are still unknown. To elucidate the

metabolic response of this disease, particularly, photosynthesis inhibition shown in infected

plants, we reconstructed PstM1, a genome-scale metabolic network of the S. tuberosum leaf.

This metabolic network is used to simulate the effect of potato late blight in the leaf

metabolism. PstM1 accounts for 2765 genes, 1113 metabolic functions, 1771 gene-protein-

reaction associations and 1938 metabolites involved in 2072 reactions. The model

optimization for biomass synthesis maximization in three infection times suggests a

suppression of the photosynthetic capacity related to the decrease of metabolic flux in light

reactions and carbon fixation reactions. In addition, we were also able to identify a variation

pattern in the flux of carboxylation to oxygenation reactions catalyzed by RuBisCO, likely

associated to a defense response in the compatible interaction between P. infestans and S.

tuberosum.

Keywords: Late blight, Phytophthora infestans, Solanum tuberosum, systems biology,

metabolic model, flux balance analysis.

10 A Genome-Scale Metabolic Model of Potato suggests a mechanism of photosynthetic

suppression during the compatible interaction with Phytophthora infestans

1.1 Introduction

Plants use various strategies to resist pathogen attack and avoid the development of diseases

[64]. In those cases, plants are considered as resistant to that specific disease, and pathogens

are referred to as avirulent on that plant. The whole plant-pathogen interaction is thus known

as incompatible. On the other hand, sometimes plant pathogens develop strategies to evade

plant defense responses, become virulent and establish the disease. In those cases, the plant-

pathogen interaction is known as compatible and the infected plant is considered as non-

resistant or susceptible [8], [9].

For some plant pathogens these evasion mechanisms are, at least, partially known [64],

however for some others these mechanisms are still obscure. The latter is the case of

Phytophthora infestans, one of the most destructive pathogens of Solanum tuberosum. This

hemi-biotrophic plant pathogen is the causing agent of the disease known as Late Blight of

Potato, the same plant disease responsible for the Irish famine in the mid-nineteenth century

[1]. S. tuberosum is the fourth most important food crop (after corn, rice, and wheat) for

human consumption [11], and it is one of the most produced crops worldwide. Historically,

potato late blight is the main factor affecting potato crop production [13], [14]. After its first

pandemic in the middle of the XIX century, P. infestans has been the most destructive

pathogen in plantations of this crop, leading to annual losses that could be enough to feed

several hundred million people [15]. The economic value of this loss and the cost of crop

protection is estimated at 6.7 billion dollars a year [16].

Even though computational modeling of potato late blight has been studied since the early

1950s, it was not until recent years that important molecular information to feed these

models was accessible to the research community. Typically, this information has been

gathered by heterogeneous approaches, which have covered several research fields, such as

structural and comparative genomics, protein-protein interactions and differential gene

expression [17]. In particular, in the field of gene expression, several investigations have

been developed with microarrays based on cDNA clones [19], transcriptome analysis

through DeepSAGE [29] and RNA-Seq analysis [18].

Capítulo 1 11

These approaches have generated large amounts of data and have allowed us to partially

understand some of the main mechanisms involved in potato late blight. Nevertheless, due

to the heterogeneity of this information, our view of the disease is still fragmented. Thus, in

order to better understand the molecular mechanisms underlying the compatible interaction

inside the host cell, it is highly convenient and necessary to gather and integrate this

information into a single computational model of the disease. This model should capture the

time-dependent nature of this biological system, integrate various ranges of spatial and

temporal scales, and allow us to explore the possible molecular mechanisms underlying the

compatible interaction.

In recent years, the scientific community has undergone multiple efforts to integrate

functional genomic characterization and biochemical knowledge into models known as

genomic-scale metabolic reconstructions (GEMR), which are based on a detailed knowledge

of the system’s individual components (functional annotation), in order to perform the

reconstruction through a Bottom-up approach, with the aim of understanding the properties

that arise from the interactions between the metabolic system’s components, and how these

behave through time and in response to environmental stimuli [46], [65]–[67].

During the past years, this approach has been widely implemented in plants, with the

development of GEMRs for several species, including Arabidopsis thaliana [47], [48], [62],

[68], Hordeum vulgare [49], Zea mays [52]–[54], Sorghum bicolor [52], Saccharum

officinarum [52]; Brassica napus [55], [56], Oryza sativa [57], and Solanum lycopersicum

[58]. In general, the development of these models can be synthesized into four fundamental

steps: 1) automatic reconstruction based on a genome annotation and biochemical databases;

2) manual refinement of the reconstruction through a literature review and biochemical and

metabolic databases. In this step, each gene and reaction are verified, so that they are

correctly located and connected; 3) mathematical and computational formalization of the

biochemical information, where the system’s specific conditions and limits are defined, this

model is validated through multiple iterations and is used to prospectively simulate the

system’s phenotypic behavior; and 4) verification, evaluation, and validation of the



reconstruction, in other words, the model’s capacity to synthesize, for example, biomass

precursors, is evaluated. Generally, this evaluation leads to the identification of incorrect

metabolic functions in the reconstruction (network gaps), which are once again evaluated

by steps 2 and 3. Therefore, the whole process is iterative and the model is generally

susceptible to being continually refined [69].

Once the mathematical model is generated in step 3, the phenotypic predictions of the

organism’s metabolic activity can be established through modelling methods based on

restrictions, which include an in silico simulation of the model under inferred metabolic

objectives and a set of restrictions that represent genetic or environmental conditions [70],

[71]. A widely used method is flux balance analysis (FBA), which performs the linear

optimization of a metabolic network in steady-state, in order to predict an optimal set of flux

values that are coherent with the maximization or minimization of the chosen objective

(which will depend on the purpose of the study) and under restrictions imposed on the

reaction fluxes [41].

Given that genomic information used to generate the metabolic reconstructions does not

consider the real expression of each gene or the subcellular localization of gene products,

flux restrictions based on different “omics” data (such as transcriptomics, proteomics, and

metabolomics) must be integrated into the GEMRs, in order to recreate specific metabolic

phenotypes [54], [59], [63]. This approach has a powerful reach for gaining knowledge of

the molecular and biochemical mechanisms of plants under specific environmental or

genetic conditions. In addition, this approach allow us to contextualize high-throughput data

as well as to guide hypothesis-driven discovery or to identify novel network properties [46].

In this study, we report the first genome-scale reconstruction of S. tuberosum and generate

a genome-scale metabolic model of the compatible interaction between S. tuberosum and P.

infestans, through the incorporation of expression data of the pathosystem into the model

(see Materials and Methods for details). Previous work on the compatible interaction has

already identified a decrease in photosynthetic activity of infected plants, however, the

Capítulo 1 13

underpinnings behind it remain unknown [19]. Hence, this model was aimed to follow up

on those findings and try to understand the molecular basis of this typical photosynthesis

turn off during plant disease. Furthermore, the model will be useful for understanding other

molecular mechanisms involved during the pathosystem and for proposing novel directed

hypotheses, guiding research in order to conduct metabolic engineering in the plant, and

identifying emerging properties of the compatible interaction, which could otherwise not be

observed through the study of individual molecules and processes.

1.2 Results and discussion

The reconstruction of the genome-scale metabolic model follows six major steps: (1)

automatic reconstruction of draft network via homology searches for the identification of

metabolic activities and biochemical reactions; (2) manual and semiautomatic refinement of

the reconstruction (3) establishment of gene-protein-reaction (GPR) association; (4)

generation of a genome-scale metabolic model in steady state; (5) incorporation of gene

expression data of the compatible interaction plant-pathogen into the metabolic model; (6)

flux balance analysis using objective function. In addition, model predictions are contrasted

against experimental observations.

1.2.1 Metabolic reconstruction

The draft network included 1288 reactions and 1482 metabolites, 217 of which were dead-

ends that decreased the metabolic network’s connectivity. A manual search of these

metabolites allowed us to identify 448 biochemical reactions, with biological and/or

genomic evidence for potato, which refined 40 metabolic pathways totally or partially,

including glycolysis/gluconeogenesis, pyruvate metabolism, glyoxylate and dicarboxylate

metabolism (photorespiration module), oxidative phosphorylation, carbon fixation in

photosynthetic organisms, amongst others (Supplementary Table 1-2). Additionally, based

on previous reports, we manually reviewed complete or partial pathways that induced a

defense response in the plant, such as those related to accumulation of salicylic acid

(ubiquinone and other terpenoid-quinone biosynthesis) and jasmonic acid (alpha-Linolenic

acid metabolism) [25], as well as other pathways related to PAMP (pathogen associated



molecular patterns) signaling cascades (Supplementary Table 1-2). By implementing

automatic-specific gap filling and semiautomatic-specific gap find and gap fill, we were able

to include 508 reactions in the reconstruction. The manual refinement and semiautomatic

processes of the reconstruction are summarized in table 1.

Table1-1. Summary of the manual and semi-automatic refinement connectivity reconstruction

Refinement New

reactions

New

metabolites

New

pathways

Complete and

partially complete

pathways

Manual 448 215 6 42

Automatic and

Semiautomatic 508 324 x x

Total 956 539 6 42

1.2.2 General model properties

Hereby, we present a metabolic model of S. tuberosum in SBML format, hereafter denoted

PstM1 (Supplementary Data File S1). This model accounts for 2765 genes, 1113 metabolic

functions, 1773 GPR associations and 1938 metabolites involved in 87 central and

peripheral metabolic pathways and 2072 reactions, of which 1254 could carry a non-zero

flux given different objective functions and the specified biomass components. The required

enzymatic activities (according to Enzyme Commission - EC) to catalyze the reactions in

the model are shown in (Figure 1-1). Among the 2072 reactions, 2059 represent biochemical

conversions and 13 represent exchange reactions with the environment, to describe the

uptake/secretion of inorganic compounds (NO3, NO2-, Nitrile, CO2, O2, SO4

2-, H2S, PO43-,

H2O, SO42-, SeO4

2−, NH3, Fe2+) and light (photon). FBA solutions showed that the model

was able to simulate leaf biomass synthesis, which was represented by the conversions of

biomass precursors: protein (amino acids), sugars, nucleotides, cell wall (cellulose, lignin

precursors) and fatty acids (hexadecanoic acid).

Capítulo 1 15

Figure 1-1: Required enzymatic activities to catalyze the reactions in the model.

1.2.3 Metabolic phenotype analysis of the compatible interaction

between S. tuberosum and P. infestans

In this study, we evaluated the plant metabolic phenotype during the first several hours and

days of compatible potato late blight interaction. Biomass synthesis was selected as the

objective function, because generally the mode of penetration of P. infestans in potato

foliage is direct, through the epidermal cells [72]–[74], where the main method of entry is

into the leaves [75].

To determine the metabolic profile for each infection time, we performed a FBA with flux

boundaries established from the gene expression data (see Methods). Our study evidenced a

decrease in the objective function (biomass synthesis of leaf) during the compatible

interaction: 28% one day post inoculation (dpi) and 33% at 3dpi, from the initial time 0dpi

(Figure 1-2). These model predictions can be understood if we take into account that for the

first interaction days, the pathogen grows well intercellularly and then intracellularly [19],

[72] mainly in the leaves [2]. We hypothesize that this pathogenic invasion causes loss of

metabolic reactions capacity of the primary metabolism to synthesize macromolecules in the

leaf and therefore in whole plant. The plants absorb water and minerals from the soil through

their root system. These organic nutrients are translocated upward through the xylem until

the leaves. All organic nutrients of plants are produced in the leaf cells, following

photosynthesis, and are translocated downward and distributed to all the living plant cells.

33%

31%

16%

8%

3%4%

5%EC 1OxidoreductasesEC 2TransferasesEC 3HydrolasesEC 4LyasesEC 5IsomerasesEC 6Ligases



When a pathogen destroys part of the photosynthetic tissue of plants and causes reduced

photosynthetic output, this often results in smaller growth of these plants and smaller yields

[76].

Figure 1-2: Metabolic fluxes of the biomass synthesis and noncyclic photophosphorylation reactions

during compatible interaction between S. tuberosum and P. infestans. The flux reaction of biomass

synthesis and noncyclic photophosphorylation decrease at 1 dpi and 3dpi.

1.2.4 Photosynthesis and carbon fixation metabolism |

Photophosphorylation, the synthesis of ATP in photosynthesis, occurs in chloroplasts [77].

Noncyclic photophosphorylation requires photosystem I and photosystem II, and involves

water oxidation, oxygen evolution and reduction of an acceptor. In contrast, cyclic

photophosphorylation is driven only by photosystem I, works with light of wavelengths over

680 nm, and does not require water oxidation and oxygen evolution [78]. S. tuberosum

PstM1 includes the definition of the following balanced photosynthetic light reactions taken

from literature sources [57], [79], [80]:

7 Photon[c] + 3 ADP[c] + 3 Orthophosphate[c] => 3 ATP[c]

0

0,2

0,4

0,6

0,8

1

1,2

1,4

1,6

1,8

0dpi 1dpi 3dpi

Met

abo

licFl

ux

mm

ol/

gdw

/h

Infection Times

Biomass synthesis Noncyclic photophosporylation

Capítulo 1 17

(1-1)

28 Photon[c] + 9 ADP[c] + 7 NADP+[c] + 9 Orthophosphate[c] + 9 H2O[c] => 7

Oxygen[c] + 7 H+[c] + 7 NADPH[c] + 9 ATP[c]

(1-2)

Our results showed that the metabolic flux for noncyclic photophosphorylation lightly

diminished through infection times (Figure 1-2) and the flux for the cyclic

photophosphorylation reaction was consistently zero. The cyclic photophosphorylation

reaction supplies only ATP, and the participation of this reaction in CO2 assimilation is

needed because the ATP formed in noncyclic reaction alone is insufficient for CO2

assimilation to the level of carbohydrate [81]. The results suggested that during the

interaction there was a reduction in the metabolic capacity of noncyclic

photophosphorylation, and cyclic phosphorylation cannot supply the ATP deficit. These

light reactions in a healthy plant convert light energy into chemical energy that is used for

many cellular reactions that contribute to biomass synthesis [82], [83]. The low capacity in

light reactions observed here could affect the flux of precursor reactions of biomass and,

consequently, affect the capacity to synthesize biomass in the model. However, the flux of

noncyclic photophosphorylation decreased less than biomass synthesis, which could be

explained by the energy from photophosphorylation that is consumed by maintenance

reactions. Some of these are associated with growth, for example, to maintain the

electrochemical gradients across the plasma membrane, whereas others are independent of

the specific growth rate of the cells [83]

The ATP formed at the expense of light energy in both cyclic and noncyclic

photophosphorylation is used for converting C02 into carbohydrates [81]. The decrease in

photosynthetic ability during compatible interaction between P. infestans and S. tuberosum

has been reported in other studies. For example, the decline in the efficiency of photosystem

II [84] and downregulation of genes encoding proteins involved in photosynthesis [19]. In

the optimization of the metabolic network in steady state, we are able to predict the reaction

flux, which is the overall rate of metabolite conversion [85]. [85]. We evaluated the fluxes

distribution of the fixation carbon pathway to evaluate the photosynthetic capacity of the



plant during the infection times. The corresponding metabolic flux distribution patterns are

shown in (Figure 1-3). A table listing the simulated flux values for each infection time is

given in Supplementary Table 1-3.

In general, the metabolic fluxes in the carbon fixation cycle (also known as the Calvin cycle)

during potato late blight is characterized by the decrease and loss of reaction fluxes

necessary to convert the inorganic carbon in organic carbon (Figure 1-3). At 0 dpi, the

metabolic fluxes of the reactions in the fixation carbon cycle varied between 5.79 and 51.42

mmol/gdw/h, suggesting interconversion of metabolites in all reactions in this pathway. At

1 dpi and 3 dpi, the variation of the metabolic fluxes in response to the compatible interaction

was from 0 to 28 mmol/gdw/h and from 0 to 25.7 mmol/gdw/h, respectively. At 3 dpi, six

reactions completely lost their flux capacity, showing a higher decrease of the global

metabolic capacity in this time compared with the two previous times of infection.

The Calvin cycle involves three main phases: 1) carboxylation of ribulose-1,5-bisphosphate

(RuBP) to form 3-phosphoglycerate (PGA), mediated by Ribulose-1,5-bisphosphate

carboxylase/oxigenase enzyme (RuBisCO); 2) reduction of PGA to the level of a sugar

(CH2O) by formation of glyceraldehyde 3-phosphate (GAP) using NADPH an ATP

produced in the light reactions; and 3) the regeneration of RuBP [86]. Hereafter, these stages

are described for the three times of infection and the subsequent changes in the metabolic

behavior are specified.

The highest flux of carboxylation of RuBP was obtained in the model optimization of 0 dpi

(Figure 1-3a). At this time, we observed that the RuBisCO enzyme had the best carboxylase

activity. In contrast, at 1 dpi, this enzymatic activity decreased, but increased the oxygenase

activity of the RuBisCO, reducing the energy efficiency of photosynthesis in the plant [87],

[88].

The subsequent metabolism of glycolate produced by the oxygenation of the RuBP is known

as photorespiration, and is associated with high light intensity, uptake of O2 and increased

Capítulo 1 19

H2O2 production [89], [90]. In the solution of this metabolic model at 1 dpi the uptake of

photons is not enhanced, but H2O2 production is increased, which is one of the major and

the most stable reactive oxygen species (ROS) that regulates basic acclamatory,

developmental and defense processes in plants [91], including programmed cell death (PCD)

[92].

One of the most rapid defense responses against pathogen attack is the oxidative burst, which

consists of the production of ROS, primarily superoxide and H2O2, at the site of attempted

invasion [93]. The quick generation of H2O2 in potato tuber tissue following inoculation

with P. infestans was previously reported [94]. Our results suggested that the increase in

photorespiration compared to the decrease in carboxylation of RuBP can be associated to

the plant’s need to trigger a quick defense mechanism, given that photorespiration would

appear to be the fastest process for generating H2O2 [95].

At 3 dpi, the oxygenation of the RuBP flux reaction disappeared, allowing an increase in the

carboxylase activity of the RuBisCO. However, the flux of the carboxylation reaction was

reduced by 55% compared to 0 dpi. Despite of the defense response through the oxidative

burst observed in the previous time, the metabolic flux to H2O2 production here was zero.

During incompatible plant- pathogen interaction, an initial and very rapid accumulation of

H2O2 is followed by a second and prolonged burst of H2O2 production. In addition, the

activity and levels of the ROS detoxifying enzymes are suppressed by salicylic acid (SA)

[96]. The suppression of ROS detoxifying mechanisms is crucial for the induction of PCD

[97], [98], which potentially limits the spread of disease [99]. In our model optimization,

only one peak of H2O2 production occurs (Figure 1-3b). Interestingly, this behavior has been

reported during compatible plant-pathogen interaction [100]. In addition, the metabolic flux

that represents the synthesis of SA in PstM1 is consistently zero at the time points of

infection evaluated. This can indicate that ROS-scavenging mechanisms are not

downregulated in the metabolic model. Thus, just one peak of

Figure 1-3: Metabolic flux distribution patterns of the fixation carbon pathway and some reactions

associated with photorespiration and carbohydrate synthesis. (a) Metabolic flux distribution patterns



for 0dpi; (b) metabolic flux distribution patterns for 1 dpi; and (c) metabolic flux distribution patterns

for 3 dpi.

oxidative burst observed at 1 dpi is not sufficient to trigger an effective defense response in

the plant; first, because a prolonged production of H2O2 is required, and second, because

CO2Bondary

H2O

Glycerate-3P

1-3 biphosphoglycerate

Glyceralde-hyde 3P

Fructose 6PErythrose 4-PSedoheptulose1,7-P2

Sedoheptulose7-P

Ribose 5P

Ribulose 5P

Ribulose 5P

Ribose

Glycerone P

Gluconeo-genesis

Starch

Xylulose 5P

Foto-respiration

H2O2

Ribulose1,5-P2

Fructose1,6-P2

CO2Bondary

H2O

Glycerate-3P


Glyceralde-hyde 3P


Sedoheptulose7-P

Ribose 5P

Ribulose 5P

Ribulose 5P

Ribose

Glycerone P

Gluconeo-genesis

Starch

Xylulose 5P

Foto-respiration

H2O2

Ribulose1,5-P2

Fructose1,6-P2

CO2Bondary

H2O

Glycerate-3P


Glyceralde-hyde 3P


Sedoheptulose7-P

Ribose 5P

Ribulose 5P

Ribulose 5P

Ribose

Glycerone P

Gluconeo-genesis

Starch

Xylulose 5P

Foto-respiration

H2O2

Ribulose1,5-P2

Fructose1,6-P2

(a)

(b)

(c)

Photo-respiration

Photo-respiration

Photo-respiration

Capítulo 1 21

ROS production without suppression of ROS detoxification does not result in the induction

of PCD [97], [98].

In the reaction of GAP formation, the fluxes fall deeply from 0 dpi to 1 dpi (Figure 1-3),

where the anabolic capacity of this reaction is null. At 3 dpi, the metabolic flux increased

incipiently, likely due to the recovery of carboxylation of the RuBisCO. The GAP molecules

can be used for the synthesis of sucrose or starch, and alternatively can be used to regenerate

RuBP [86], [101]. We compared the fluxes of the starch synthesis reaction with the fluxes

of PGA transformation in GAP through all time points of infection, based on the idea that

starch production is a good indicator of a healthy plant, which will only store extra reservoirs

of starch in tissues if all their energy requirements are already fulfilled [102]. In addition,

starch has been identified as an important integrator in plant growth regulation to cope with

continual changes in carbon availability when the rate of photosynthesis is modified by

environmental constraints [102], [103]. The comparison between these two reactions

showed the same change trend in metabolic fluxes (Figure 1-4). At 1 dpi, the metabolic flux

to synthesize GAP and starch is the lowest, and at 3 dpi, the flux of this reaction increased

incipiently. Our results indicated that the loss of carbon fixation capacity of the RuBisCO

and the subsequent decrease in GAP formation from PGA, can be related to the decreased

efficiency of starch biosynthesis.

Previous studies have shown that starch biosynthesis regulation is linked with the expression

of ADP-Glc pyrophosphorylase (AGPase) in leaves [103], [104]; likewise, AGPase activity

is generally activated by PGA [105]. Therefore, AGPase activation or inactivation by PGA

production allows starch synthesis to be adjusted in response to changes in photosynthesis

[106]. We found that the metabolic flux of the AGPase activity decreased slightly through

infection times (view Supplementary Table 1-3). This can be associated with the general

decline in the efficiency of starch synthesis in response to the decrease of biosynthesis of

GAP from PGA. Although the AGPase activity and starch biosynthesis both tend to

decrease, they show particular tendencies that are not comparable between them, especially

from 1 dpi to 3 dpi (view Supplementary Table 1-3). Hence, additional regulatory



mechanisms are required to achieve changes in the rate of starch biosynthesis, as previously

reported [103], [107]–[110].

Figure 1-4: Metabolic fluxes of GAP formation and starch synthesis. The fluxes of these reactions

showed the same trend through infection time.

In the Calvin cycle, the RuBP is both consumed and synthesized [111]. The synthesis of

RuBP is known as regeneration, and involves a series of reactions from GAP, that are

energetically favorable and do not consume ATP or NADPH, except in the phosphorylation

reaction to transform ribulose 5-phosphate into RuBP [112]. The fluxes distribution of these

reactions are affected during compatible interaction (Figure 1-3) mainly at 3 dpi, where a

null flux is obtained for three reactions. The net flux of transformation of ribulose 5-

phosphate in RuBP reaction decreases approximately by 55% at 1 dpi and 3 dpi compared

to 0 dpi. This can be a consequence of both the decrease in the metabolic flux of its

precursors reactions in the cycle as well as in the decrease of the metabolic capacity of ATP

production for the light reactions. In addition, we observed that at 0 dpi and 3 dpi the

metabolic fluxes of the regeneration and carboxylation of RuBP are directly proportional.

At 1 dpi, the metabolic flux of the regeneration was directly proportional to the sum of the

flux for carboxylation and oxygenation. Overall, these results can indicate that in our model

Capítulo 1 23

the RuBP is synthetized in the same rate that it is consumed. This observation agrees with

previous studies that demonstrated that, in a photosynthetic steady state model, the rate at

which RuBisCO consumes RuBP equals the rate at which RuBP is regenerated [113], [114].

1.3 Conclusions

In this work, we simultaneously introduced the first metabolic network of S. tuberosum and

the first genome-scale metabolic model of the compatible interaction of a plant with P.

infestans. The metabolic flux of the light reactions and carbon fixation cycle, including

photorespiration and starch synthesis, suggest a suppression of the photosynthetic capacity

as consequence of the compatible interaction between P. infestans and S. tuberosum. The

results shown here are in silico metabolic predictions, which closely match previous studies

of plant physiology. We recommend the compartmentalization of the model for a better

evaluation of flux between cellular organelles.

1.4 Materials and Methods

1.4.1 Metabolic reconstruction.

An initial automatic draft reconstruction was first created by means of Subliminal [115] and

RAVEN [116] software toolboxes starting from the PGSC potato genome sequence [30].

Both automatic reconstructions were then conciliated and merged through in-house

scripting. This merged reconstruction was taken as a starting point for manual reconstruction

and then subjected to a manual refinement based on literature and available biological data.

1.4.2 Metabolic reconstruction refinement

The reconstruction refinement stage was divided into six phases: (1) manual gap refinement

of the metabolic network and manual refinement of the reversibility and directionality of the

reactions; (2) automatic-specific filling; (3) semiautomatic-specific gap find and gap fill; (4)

establishment of the directionality and reversibility of the reactions through Gibbs free

energy of reaction value (ΔrG′°) [117]; (5) inclusion of exchange reactions; and finally (6)

gene-protein-reaction associations (Figure 1-5).



Figure 1-5: General scheme of the refinement of potato metabolic network. The lines indicate the

trajectory from data sources to the refined metabolic network.

During manual refinement, the network’s connectivity was verified in a pathway by pathway

basis, as well as in a metabolite by metabolite basis [69]. For this, a search for dead-end

metabolites in the reconstruction was performed by means of the R package minval [118];

these metabolites corresponded to those that are consumed in the set of biochemical

reactions, but are not synthesized and viceversa. Based on the identified dead-end

metabolites, missing reactions in the reconstruction were manually tracked within the

KEGG Pathway Maps database [119], [120], which associates organism-specific genomic

information to metabolic pathways maps. For reactions not reported for S. tuberosum in the

KEGG Pathways database, we verified that their catalyzing enzymatic activity was reported

in the Plant Metabolic Network (PMN) database specific for potato (PotatoCyc)

(http://pmn.plantcyc.org/POTATO/organism-summary). In addition, based on biochemical

literature, carbohydrate and energetic metabolic pathways were further refined. During the

entire manual review process of the network’s connectivity, reactions without any type of

biological and/or genomic evidence for this plant were removed, and the reversibility and

directionality of 120 reactions were corrected.

KEGG

PotatoCyC

MetaCyC

eQuilibrator

Semiautomatic-specific gap fin and gap fill

Automatic-specific filling

Manual Refinement

Assignment of thermodynamic contraints

Reaction Stoichiometry

Reaction Directionality

Gen-Protein-Reaction

association

Data sources Methods Metabolic Network

Literature

Capítulo 1 25

In order to verify that the metabolic pathways reported in this reconstruction were present

in the metabolism of S. tuberosum, we implemented the KEGGREST R package, which

allows to obtain all of the metabolic pathways reported for this organism in the KEGG

pathways database [121]. By comparing the metabolic pathways obtained from KEGG with

those in the reconstruction, we found 12 non-reported pathways, which were then removed.

Since some of the reactions belonging to these pathways were catalyzed by enzymatic

activities reported in PotatoCyc, these were included in the reconstruction without being

associated to any specific metabolic pathway.

During the process of automatic-specific filling, a database construction of all the

biochemical reactions reported for S. tuberosum in KEGG was done using the g2f R package

[122]. Later, only missing reactions were added to the reconstruction, using the sot_g2f in-

house script (available in GitHub: https://github.com/kellybotero/PotatoRecon). Since the

network still showed gaps, a semiautomatic-specific gap finding and gap filling process was

performed using the g2f package. For this, once again we identified all of the dead-end

metabolites in the network and automatically tracked them to a reference database that

contains all of the biochemical reactions stored in KEGG. The gap fill search method was

restricted to retrieve only reactions that showed metabolites in the reconstruction. Finally,

through manual validation, we included only reactions with enzymatic activities reported

for S. tuberosum in PotatoCyc.

The reversibility and directionality of the reactions that were not manually corrected were

determined through ΔrG′° values obtained from EQuilibrator [123] and MetaCyc [124]

databases. These databases establish the value for ΔrG′° by calculating the Gibbs free energy

of formation of a compound (ΔfG′°), through the group contribution method for

thermodynamic analysis [117]. The parameters used to calculate ΔfG′° in Equilibrator are

pH 7.0 and ionic strength 0.1, and in MetaCyc these are pH 7.3 and ionic strength 0.25.

Since the parameters are located in a pH range of 7.0 – 7.3 and ionic strength of 0.1 – 0.25,

the reversibility R script (available in GitHub: https://github.com/kellybotero/PotatoRecon)

was implemented, which allowed us to compared the ΔrG′° values from both databases.



When both reversibilities were below -1 (integrated open framework for thermodynamics

of reactions that combines accuracy and coverage), the GEMR reversibilities were

established as forward irreversible. Due to lack of biological evidence and discrepancies

between the ΔrG′° values of the databases, the remaining reactions were determined as

reversible.

During the fifth phase of the reconstruction refinement process, we included 13 exchange

reactions which transport metabolites that cannot by synthesized by the cell, within the limits

of the system to the cytoplasm, and are precursors to other metabolites [48]. Finally, once

the reconstruction was refined in terms of its reactions, metabolic pathways and reversibility,

GPR associations were integrated using the g2f package. This package constructs GPRs

based on KEGG ORTHOLOGY of the reactions present in the reconstruction.

1.4.3 Transformation of the reconstructed network into a genome-scale

metabolic model

From the genome-scale metabolic reconstruction of potato, a SBML version was generated

using the R package minval. Consecutively, the SBML file was imported to the R package

Sybil [125], where the whole set of reactions present in metabolic reconstruction was

transformed into a steady state metabolic model Sij.vj=0. Where Sij is the entries of the

stoichiometric matrix (Supplementary Data File S2). Rows in S represent metabolites and

columns represent reactions, and vj is the metabolic flux vector for each reaction. Substrates

in the reaction have negative coefficients, while products have positive ones. This matrix

also takes into account transport reactions across the cell membrane, which are represented

as reactions interconverting intracellular and extracellular compounds. In the metabolic

model, the reaction fluxes are subject constrains (- vjmin ≤ v ≤ vjmax ) [49], [126].

Objective function was defined by the biomass synthesis reaction in the leaf OFbioamass

(Supplementary Data File S2), previously reported in the genome-scale metabolic model of

Arabidopsis thaliana [68]. This objective function was mathematically written as a

Capítulo 1 27

combination of metabolic coefficients of the biomass composition estimated for slow-

growing species [127], [128].

1.4.4 Incorporation of gene expression data into the genome-scale

metabolic model

Gene expression data of the compatible interaction were obtained from a study of Gyetvai

et al., 2012. We used the normalized libraries of the untransformed cultivar Désireé at three

infection time points with P. infestans (zero (0 dpi), one (1 dpi) and three (3 dpi) days post

inoculation), with three biological replicates. The tag annotation was performed by

BLASTN [129]. The source for the tag annotation was the available RNA sequence of

“Potato 3.0” (ftp://ftp.ncbi.nlm.nih.gov/genomes/all/GCF_000226075.1_SolTub_3.0/). The

unique genes and maximum value counts per gene were performed with the script

summarization.r (available at GitHub: https://github.com/kellybotero/PotatoRecon). As the

last step for building the gene expression database, all refseq gene identifiers were

transformed to Entrez identifiers , by means of the R package UniProt.ws [130].

From the previously built gene expression database, we generated an expression set for each

infection time point by means of the R package Biobase [131]. The gene expression values

were incorporated directly into fluxes constraints of the reactions in the model using the R

package ex2flux [132], which implements a method to integrate gene expression values into

each GPR associated to the reactions of the model.

1.4.5 Metabolic flux model optimization

FBA represents a constraint-based modeling approach that allows the prediction of

metabolic steady-state fluxes, by applying mass balance constraints into a stoichiometric

model (Varma and Palsson, 1994). The reactions in the model can be represented by a linear

system of equations, then, problems such as maximizing specific chemical production or

growth can be solved by linear programming [46], [133]. With the purpose of obtaining a

computational distribution of metabolic fluxes, FBA was employed assuming maximization

of the objective function, by means of the R package Sybil (Equation. (1-3)).

ftp://ftp.ncbi.nlm.nih.gov/genomes/all/GCF_000226075.1_SolTub_3.0/



maximization OFbioamass

subject to

∑ Sij.vj=0

i = 1,2…m j =1,2…n

- vjmin ≤ v ≤ vjmax

(1-3)

To constrain the space of all the possible steady-state flux distributions in the optimization

we impose thermodynamic constraints to reaction reversibility as well as upper and lower

bounds constraints on reactions fluxes from known expression values for the particular

enzyme that catalyzes the reaction.

Capítulo 1 29

1.5 Supplementary

Supplementary Table 1-2: Refined pathways in the metabolic network reconstruction. We show

all the pathways included in the metabolic network of S. tuberosum. Pathway association was

assigned based on the categorization of the KEGG Pathways database. The colors correspond to the

level of curation of each pathway

Alpha-Linolenic

acid

metabolism

Arginine and

proline

metabolism

Ascorbate and

aldarate

metabolism

Carbon fixation

in

photosynthetic

organisms

Citrate cycle

(TCA cycle)

Flavonoid

biosynthesis

Galactose

metabolism

Inositol

phosphate

metabolism

Nitrogen

metabolism

Oxidative

phosphorylation

Photosynthesis

(ligth reactions)

Porphyrin and

chlorophyll

metabolism

Pyruvate

metabolism

Steroid

biosynthesis

Sulfur

metabolism

Alanine,

aspartate and

glutamate

metabolism

Benzoxazinoid

biosynthesis

Brassinosteroid

biosynthesis

Carotenoid

biosynthesis

Cyanoamino

acid

metabolism

Cysteine and

methionine

metabolism

Diterpenoid

biosynthesis

Fructose and

mannose

metabolism

Glutathione

metabolism

Glycerolipid

metabolism

Glycerophosph

olipid

metabolism

Glycolysis /

Gluconeogenes

is

Glyoxylate and

dicarboxylate

metabolism

Histidine

metabolism

Lysine

biosynthesis

Lysine

degradation

Other types of

O-glycan

biosynthesis

Pantothenate

and CoA

biosynthesis

Propanoate

metabolism

Selenocompo-

und

metabolism

Sphingolipid

metabolism

Starch and

sucrose

metabolism

Terpenoid

backbone

biosynthesis

Ubiquinone

and other

terpenoid-

quinone

biosynthesis

Zeatin

biosynthesis

Thiamine

metabolism

Amino sugar

and nucleotide

sugar

metabolism

Biosynthesis of

unsaturated

fatty acids

Butanoate

metabolism

Caffeine

metabolism

Carbon

metabolism

Fatty acid

elongation

Fatty acid

metabolism

Glycine, serine

and threonine

metabolism

Linoleic acid

metabolism

Monoterpenoid

biosynthesis

Pentose

phosphate

pathway

Phenylalanine

metabolism

Phenylalanine,

tyrosine and

tryptophan

biosynthesis

Phenylpropano

id biosynthesis

Purine

metabolism

Pyrimidine

metabolism

Tryptophan

metabolism

Valine, leucine

and isoleucine

biosynthesis

Aminoacyl-

tRNA

biosynthesis

Anthocyanin

biosynthesis

Arachidonic

acid

metabolism

Arginine

biosynthesis

beta-Alanine

metabolism

Biotin

metabolism

Ether lipid

metabolism

Fatty acid

biosynthesis

Flavone and

flavonol

biosynthesis

Folate

biosynthesis

Glucosinolate

biosynthesis

Glycosaminogl

ycan

degradation

Glycosphingoli-

pid

biosynthesis -

globo series

Glycosylphosph

atidylinositol

(GPI)-anchor

biosynthesis

Lipoic acid

metabolism

Limonene and

pinene

degradation

N-Glycan

biosynthesis

Nicotinate and

nicotinamide

metabolism

One carbon

pool by folate

Pentose and

glucuronate

interconversio

ns

Riboflavin

metabolism

Stilbenoid,

diarylheptanoid

and gingerol

biosynthesis

Synthesis and

degradation of

ketone bodies

Taurine and

hypotaurine

metabolism

Tropane,

piperidine and

pyridine

alkaloid

biosynthesis

Tyrosine

metabolism

Valine, leucine

and isoleucine

degradation

Vitamin B6

metabolism

Complete Partially complete Intervened Not intervened



Supplementary Table 1-3: Reaction fluxes of the metabolic pathways of interest in S. tuberosum

to evaluate photosynthetic capacity through compatible interaction with P. infestans.

Pathways Reaction

(ID

KEGG)

Metabolic

flux (0 dpi)

Metabolic

flux (2 dpi)

Metabolic

flux (3 dpi)

Biomass Synthesis RBS01 1,313856 0,9435836 0,8790459

Cyclic Photophosphorylation RK0004 0 0 0

Non Cyclic Photophosphorylation RK0005 1,630357 1,408214 1,35

Carbon Fixation

R00024 46,38961 14,34539 25,7072

R01512 19,59667 0 0

R01061

*inv -45,65 5,326667 -1,176667

R01015 17,39 8,923333 0

R01068

*inv -5,79 -13,63667 0

R00762 5,79667 13,63667 0

R01067 5,79667 13,63667 0

R01829 5,79667 12,67667 0

R01845 5,79667 12,67667 13,94333

R01641 25,52 12,91333 10,93469

R01056 -5,036667 -2,386667 -2,251979

R01523 46,3891 25,61669 25,7072

R01529

*inv -51,426 -28,00336 -25,65781

R01051 -5,036667 -3.62 -5,69

Photorespiration

R03140 0 11,2713 0

R01334 0 11,2713 0

R00475 0 39,43 0

R00009 0 36,37207 3,992193

R00372 0 0 65,06771

R00945 -40,9 2,556667 -2,646667

R01221 28,57 10,43925 14,86955

R00588 693,29 1543,01 854,7267

R01388 -4,417 -3,146667 -19,57333

R01514 0 0 0

AGPase activity R00948 0.3481719 0.2500497 0.2329472

Starch Synthesis R02110 26,29711 0,25 5,42

Salicylic Acid Synthesis RK0003 0 0 0

* inv = The direction of the metabolic flux in the metabolic pathway is inverted

2. Finding and filling gaps in metabolic networks

through the ‘g2f’ R package

. Original title: g2f: An R package for finding and filling gaps in metabolic networks.

Abstract

During the construction of a genome-scale metabolic network reconstruction, several dead-

end metabolites which cannot be imported/produced, or that are not used as substrates or are

released by not any of the reactions are incorporated into the network. The presence of dead-

end metabolites can block the net flux of the objective function when it is evaluated through

Flux Balance Analysis (FBA), and when it is not blocked, then the bias in the biological

conclusions increases. The refinement to restore the connectivity of the network can be

carried out manually or using computational algorithms. The ‘g2f’ package was designed as

a tool to find the dead-end metabolites, and fill it from the stoichiometric reactions of a

reference, filtering candidate reactions using a weighting function. Also, the option to

download all the set of gene-associated stoichiometric reactions for a specific organism from

the KEGG database is available.

2.1 Introduction

Genome-scale metabolic network reconstructions (GMNR) specify the chemical reactions

catalyzed by hundreds of enzymes (registered in enzyme commission – EC) and cover the

molecular function for a substantial fraction of a genome [134]. The main goal of these

network reconstructions is to relate the genome of a given organism with its physiology,

incorporating every metabolic transformation that this organism can perform [59], [116].

32 g2f: An R package for find and fill gaps in metabolic networks.

The GMNR are converted into computational models for metabolism simulation and gaining

insight into the complex interactions that give rise to the metabolic capabilities [135], [136].

The predictive accuracy of a model depends on the comprehensiveness and biochemical

fidelity of the reconstruction [137].

The GMNR construction process can be synthesized into two fundamental stages: (1) draft

network reconstruction, here the reactions associated to the enzymes that participate in the

metabolism of a particular organism are downloaded from specialized genome, biochemical

and metabolic databases; and (2) manual or computational refinement of the network.

Similar steps are performed during the construction of a tissue-specific metabolic

reconstruction, defined as subsets of reactions included in a genome-scale metabolic

reconstruction that are highly associated to the metabolism of a specific tissue. They are

constructed from measured gene expression or proteomic data and enable to characterize or

predict the metabolic behavior for each tissue under any physiological condition. Given that

only the reactions associated to an enzyme or gene can be mapped from the measured data,

spontaneous reactions and non-facilitated diffusion are missing in first stages of a tissue-

specific reconstruction.

The refinement stage of the reconstruction is a process to restore the connectivity of the

network, where network gaps in the draft reconstruction are identified, and candidate

reactions to fill the gap are found in literature and databases [69], [138]. Since network

reconstructions typically involve thousands of metabolic reactions, their refinement can be

a very complex task [116]. Network gaps can be associated to dead-end metabolites which

cannot be imported/produced by any of the reactions in the network; or to metabolites that

are not used as substrates or released by any of the reactions in the network. When the

metabolic network is transformed into a metabolic steady-state model in order to optimize

the distribution of metabolic flux under an objective function, the presence of this type of

metabolites can be problematic, since the flux cannot pass through them due to the

incomplete connectivity with the rest of the network [138]. In a high quality model, all

reactions should be able to carry flux if all relevant exchange reactions are available [116].

The lack of flux in dead-end metabolites is propagated downstream/upstream, depending if

Capítulo 2 33

the metabolites are not produced or not consumed, giving rise to additional metabolites that

cannot carry any flux [138]. This can block the net flux of the objective function and when

it is not blocked, then bias in the biological conclusions increases.

The manual refinement is an iterative process to assemble a higher confidence compendium

of an organism-specific metabolism in a draft metabolic network reconstruction [67], [139],

[140]. This type of refinement requires time and a labor intensive of use of available

literature, databases and experimental data [67], [141]. For example, if the genome

annotation of the target organism is present in KEGG [119], reactions associated to the genes

can be identified in KEGG maps and dead-end metabolites under the organism-specific

metabolic environment can be tracked [69]. Any given GMNR accounts for hundreds or

thousands of biochemical reactions, thus, this task is very complex and can lead to both the

introduction of new errors as well as the possibility of overlooking some others.

Network gaps refinement can also be performed using algorithms to identify blocked

reactions through an optimization of the metabolic model, and to fill metabolic functions

gaps, by means of searching for reactions associated to the missing functions in available

databases [116], [137]. This approach, however, only fills gaps for a single biological

objective function, while other implemented approaches based on the identification and

filling of dead-end metabolites, included in GAMS [8] and COBRA [14] packages, allow to

fill the networks gaps for all of the metabolism, generating a list of reactions that enable to

restore the network connectivity and eliminate blocked reactions that no carry flux in a

steady state model [11]. Some drawbacks, however, are that implemented COBRA [71] gap

fill algorithms operate as tools under the commercial MATLAB® environment, and GAMS

[138] only allow to perform gap fill using MetaCyc databases as reference [124].

With the aim of offering an open source tool that facilitates the refinement and depuration

of draft network reconstructions and metabolic models, we introduce the ‘g2f’ R package.

It includes four functions to identify and fill gaps, as well as, to calculate the addition cost

of a reaction, depurate metabolic networks of blocked reactions (not activated under any

scenario) and a function to associate GPR to reactions included in a metabolic reconstruction

using the KEGG database as a reference.


2.2 Installation and functions

g2f includes four functions and is available for download and installation from CRAN, the

Comprehensive R Archive Network. To install and load it, just type:

> install.packages("g2f")

> library(g2f)

The g2f package requires R version 2.10 or higher.

2.2.1 Downloading a reference from the KEGG database

The KEGG database is a collection of databases widely used as references in genomics,

metagenomics, metabolomics and other omics studies, as well as for modeling and

simulation in systems biology [16]. To date, the database includes genomes, biological

pathways and its associated stoichiometric reactions for 346 eukaryotes, 3947 bacteria, and

238 archaea. The getReference function downloads all the KO-associated stoichiometric

reactions, and their correspondent E.C. numbers from the KEGG database for a customized

organism (using the KEGG organism ID). Based on the KOs associated to a reaction, their

respective GPR is constructed as follows: All genes associated to a given KO are linked by

an AND operator, after that, when a reaction has more than one associated KO, previously

linked genes are now joined by an OR operator. As an example, to download all (1392

reactions) stoichiometric reactions associated to Escherichia coli just type:

> E.coli <- getReference(organism = "eco")

2.2.2 Calculating the addition cost

Metabolite-based reaction mapping, followed by the addition of new reactions, is a very

basic solution for a gap fill process, which can increase the number of dead-end metabolites.

As a way to reduce the addition of new dead-end metabolites, the additionCost function

calculates a cost (in terms of new metabolites) to be added, based on metabolites that

constitute the new reaction and those that constitute the stoichiometric reactions present in

the metabolic reconstruction, following the equation 2-1.

Capítulo 2 35

n(metabolites(newReaction) є metabolites(reactionList))

additionCost =

n(metabolites(newReaction)) (2-1)

As an example, we select a sample of reactions from the downloaded reference for E. coli

and calculate the addition cost for the remaining reactions (6 rst values are showed).

> reactionList <- sample(E.coli$reaction,10) > head( + additionCost(reaction = E.coli$reaction,

+ reference = reactionList)

+ )

[1] 0.4000000 0.4000000 0.4000000 0.4000000 0.3333333 0.3333333

2.2.3 Performing a gap find and fill

To identify network gaps in a metabolic network and fill them from a reference, the gap Fill

function internally performs several steps: (1) Dead-end metabolites are identified from the

stoichiometric matrix using functions included in the minval package, (2) the candidate

reactions to be added are identified by metabolite mapping, (3) the addition cost of each

candidate reaction is calculated, (4) the candidate reactions with an addition cost lower or

equal to the user-defined limit are added to the reaction list, and, finally, (5) the process

returns to step 1 until no more original-gaps can be filled under the user-defined limit. The

function returns a set of candidate stoichiometric reactions to fill the original gaps included

in the metabolic network.

As an example, we show how to fill the dead-end metabolites included in the previously

selected sample using all downloaded stoichiometric reactions from the KEGG database for

E. coli as the reference

> gapFill(reactionList = reactionList,

+ reference = E.coli$reaction, + limit = 1/4 + )

23 Orphan reactants found




11 Orphan products found

[1] "D-Mannonate + NAD+ <=> D-Fructuronate + NADH + H+" [2] "ATP + Thymidine <=> ADP + dTMP" [3] "dTTP + H2O <=> dTMP + Diphosphate" [4] "(R,R)-Tartaric acid + NAD+ <=> 2-Hydroxy-3-oxosuccinate + NADH + H+" [5] "Hypoxanthine + NAD+ + H2O <=> Xanthine + NADH + H+" [6] "Ammonia + 3 NAD+ + 2 H2O <=> Nitrite + 3 NADH + 3 H+" [7] "L-Glutamine + H2O <=> L-Glutamate + Ammonia" [8] "ATP + Deamino-NAD+ + Ammonia <=> AMP + Diphosphate + NAD+" [9] "Ammonia + NAD+ + H2O <=> Hydroxylamine + NADH + H+"

[10] "ATP + Glutathione + Spermidine <=> ADP + Orthophosphate + Glutathionylspermidine" [11] "2 Glutathione + NAD+ <=> Glutathione disulfide + NADH + H+" [12] "Glutathione + H2O <=> Cys-Gly + L-Glutamate" [13] "L-Proline + NAD+ <=> (S)-1-Pyrroline-5-carboxylate + NADH + H+" [14] "L-Glutamate 5-semialdehyde + NAD+ + H2O <=> L-Glutamate + NADH + H+" [15] "ATP + Pantothenate <=> ADP + D-4'-Phosphopantothenate"

2.2.4 Identifying blocked reactions

To identify the blocked reactions included in a metabolic model, the blockedReactions

function sets each one of the reactions included in the model (one at a time) as the objective

function and optimizes the model through Flux Balance Analysis. Reactions that do not

participate in any possible solution during all evaluations are returned as blocked reactions.

As an example, we identify the blocked reactions in the E. coli core metabolic model

included in the ‘sybil’ package.

> data("Ec_core") > blockedReactions(Ec_core)

|=====================================================================| 100%

[1] "EX_fru(e)" "EX_fum(e)" "EX_mal_L(e)" "FUMt2_2" "MALt2_2"

2.3 Summary

We introduced the g2f package to find dead-end metabolites included in a metabolic

reconstruction, and fill them from stoichiometric reactions of a reference, filtering candidate

reactions by using a weighting function and a user-defined limit. We show step by step the

Capítulo 2 37

functionality of each procedure included in the package using a reference downloaded from

the KEGG database for E. coli, and the core metabolic model included in the ‘sybil’ package.

.

3. Constraining the metabolic reconstruction:

Incorporating expression data as FBA limits

through the ‘exp2flux’ R package

Original title: exp2 ux: Convert Gene EXPression Data to FBA FLUXes

Abstract

Computational simulations of metabolism can help predict the metabolic phenotype of an

organism in response to different stimuli, through constraint-based modeling approaches.

To recreate specific metabolic phenotypes and enhance the model predictive accuracy,

several methods for integrating transcriptomics data into constraint-based models have been

proposed. The majority of available implemented methods are based on the discretization of

data to incorporate constraints into the metabolic models via Boolean logic representation,

which reduces the accuracy of physiological representations. The methods implemented for

gene-expression data integration as continuous values are very few. The exp2flux package

was designed as a tool to incorporate, in a continuous way, gene-expression data as FBA

flux limit in a metabolic reconstruction. Also, a function to calculate the differences between

fluxes in different metabolic scenarios was included.

3.1 Introduction

Metabolism is a cellular system suited for developing studies at the systemic level of the

genotype-phenotype relationship and genetic interactions [134]. Genome sequencing

projects have contributed to our understanding of the metabolic capabilities in cellular

systems since functional annotation of gene products (enzymes) allow the reconstruction of

40 exp2flux: Convert Gene EXPression Data to FBA FLUXes

genome-scale metabolic networks (GMNs) that summarize these metabolic capabilities

consistently and compactly in a stoichiometric matrix [142], [143]. GMNs can be converted

into computational models to predict the metabolic phenotype of an organism in response to

different stimuli, through constraint-based modeling approaches [70], [71]. A widely used

approach to perform in silico metabolic simulations is flux balance analysis (FBA), a linear

optimization method which uses imposed mass balance and constraints (that represent

genetic or environmental conditions) to define the space of feasible steady-state flux

distributions of the network and then identify optimal network states that maximize a defined

objective function [41], [134].

Given that steady-state simulations assume a constant enzymatic rate and does not consider

the real expression of each gene or the subcellular localization of gene products, flux

constraints based on different omics data (such as transcriptomics, proteomics, and meta-

bolomics) must be integrated into GMNs, in order to recreate specific metabolic phenotypes

and enhance model predictive accuracy [63], [144]. Integrative methods have a powerful

potential to describe molecular and biochemical mechanisms of organisms’ metabolism

under specific environmental or genetic conditions, as well as to allow contextualizing high-

throughput data [46].

Several algorithms and methods have been developed to integrate experimental data into

GMNs [145]. Given the increase of gene expression data, these algorithms have focused on

incorporating transcriptomics data into constraint-based models [146], [147] and, in this

manner, constrain flux distribution (solution space) in GMNs [71], [148]. Each of the

algorithms is based on the assumption that mRNA transcript levels are a strong indicator of

the level of protein activity [149]. The algorithms differ mainly in the way to integrate

expression data, some of the implemented algorithms incorporate data in a discrete or

continuous way, using absolute values for a single condition, or relative expression levels

between different conditions [145]. Most methods are based on the discretization of data to

incorporate constraints into metabolic models via Boolean logic representation

(activation/inactivation flux) [149]. Even when continuous integration could be more

accurate for the physiological representation of the continuity of the reactions activity

Capítulo 3 41

gradient [63], the methods of continuous integration are very few [145].

With the aim of offering an open source tool that facilitates the integration of gene-

expression data as a continuous constraint (FBA limits) in metabolic models, we introduce

the “exp2flux” R package. The exp2flux package incorporates a previously described but

not implemented continuous gene-expression data integration method [150], [151]. The

implemented method is based on the association of omics data with genes included in the

Gene-Protein-Reaction (GPR) related to each reaction in a genome-scale metabolic model

[152] and considers different possible biological scenarios that occur during the catalysis of

biochemical reactions [150][19] (Figure 3-1). Also, a function to calculate the difference in

reaction fluxes between simulated scenarios was included.

Figure 3-1: Workflow to integrate omics data into reaction flux of a genome-scale metabolic model.

0.12

0.52

??

0.95

Gene 1

Gene 2

Gene 3

Gene 4

R1

R3

R2

Mean orMedean

GPR

Enzime complex(and)

Isozymes (or)

The minimum Sumatory

0.15

0.09

0.490.21

R4


3.2 Installation and functions

exp2flux includes two functions and is available for download and installation from

CRAN, the Comprehensive R Archive Network. To install and load it, just type:

> install.packages("exp2flux") > library(exp2flux)

The exp2flux package requires R version 2.10 or higher.

3.2.1 Inputs

Functions included in the exp2flux package takes two kind of objects as input, metabolic

models as an object of class modelorg for the ‘sybil’ R package, and gene-expression data

as an object of class ExpressionSet, a container for high-throughput assays and experimental

metadata described in the ‘Biobase’ Bioconductor package.

3.2.2 Converting gene expression data to FBA limits

Gene-protein-reaction (GPR) associations indicate which gene has which function to a

genome-scale metabolic network and are represented as Boolean relationships between

genes. This function calculates and assigns the flux boundaries for each reaction based on

their associated GPR. The value is obtained as follows: (1) When two genes are associated

with an AND operator according to the GPR rule, a minimum function is applied to their

associated expression values. In the AND case, downregulated genes alter the reaction,

acting as the limiting factor in enzyme formation, since both are required for the enzymatic

complex formation. In turn, (2) when the genes are associated with an OR rule, each one of

them can code an entire enzyme to act as a reaction catalyst. In this case, a sum function is

applied for their associated expression values. For missing gene expression values, the

function does a data imputation and assigns one of: `min', `1q',`mean', `median', `3q', or

`max' expression values calculated from the genes associated to the same metabolic

pathway. Metabolic pathway assignation for each reaction is performed through an organism

specific search in the KEGG database. In the case of not being able to assign a pathway to

a gene, the value to be assigned is calculated from all gene expression values. The fluxes

Capítulo 3 43

boundaries of exchange reactions are not modified. To show the potential use of data

integration through the exp2flux function, in this example, we simulate values to represent

gene expression data and integrate it into the Escherichia coli core metabolic model included

in the ‘sybil’ R package.

Integration of gene-expression data begins by loading the ‘exp2flux’, ‘sybil’ and ‘biobase’

required packages.

> library(exp2flux) > library(sybil) > library(Biobase)

After that, the E. coli core metabolic model can be loaded from the ‘sybil’ package. The

model includes 95 biochemical reactions associated with 137 genes in 69 GPR rules.

> data("Ec_core")

Five different measures to represent the gene-expression data for each gene included in the

metabolic model was simulated, and the generated matrix was converted to an

ExpressionSet.

> geneExpression <- ExpressionSet(assayData = matrix( + data = runif(n = 5*length(Ec_core@allGenes), min = 0, max = 1000), + nrow = length(Ec_core@allGenes), + dimnames = list(c(Ec_core@allGenes)) + )) > geneExpression

ExpressionSet (storageMode: lockedEnvironment) assayData: 137 features, 5 samples

element names: exprs

protocolData: none

phenoData: none

featureData: none experimentData: use 'experimentData(object)' Annotation:

Incorporation of gene-expression data into the metabolic model through the exp2flux

function requires two objects, a metabolic model and an ExpressionSet as arguments. The

exp2flux function returns a constrained metabolic model.


> mEc_core <- exp2flux( + model = Ec_core, + expression = geneExpression + ) > mEc_core model name: Ecoli_core_model number of compartments 2

C_c C_e

number of reactions: 95 number of metabolites: 72 number of unique genes: 137 objective function: +1 Biomass_Ecoli_core_w_GAM

To visualize the metabolic changes induced by the incorporation of gene-expression data as

FBA limits of the reactions included in the metabolic model, a Flux Variability Analysis

was performed using the original E. coli core metabolic model and the constrained one.

> par(mfcol=c(1,2)) > plot(fluxVar(Ec_core),main="Original Model",ylim=c(-100,1000))

| : | : | 100 %

|===================================================| :-)

> plot(fluxVar(mEc_core),main="Modified Model",ylim=c(-100,1000))

| : | : | 100 %

|===================================================| :-)

Figure 3-2: Flux differences between an unconstrained and a constrained model. Constraints were

calculated through the exp2flux R package using simulated gene expression data.

Capítulo 3 45

3.2.3 Identifying flux changes between scenarios

The measurement of flux change for each reaction between metabolic scenarios is a task

generally carried out manually and oriented directly towards the research objective.

However, at a system level analysis, this process can become laborious. The fluxDifferences

function calculates the fold change for each common reaction between metabolic scenarios.

Fold change is a measure that describes how much a values changes going from an initial

to a final value. The algorithm implemented in the fluxDifferences functions is described in

equation 3-1; the function takes as an argument two valid models for the ‘sybil’ R package

and a customizable threshold value to filter functions to be reported.

(3-1)

As an example, we report the fold change of all reactions with an absolute change greater or


equal to 2-fold between the unconstrained and constrained metabolic scenarios previously

simulated.

> fluxDifferences( + model1 = Ec_core, + model2 = mEc_core, + foldReport = 2 + )

3.3 Summary

We introduced the exp2flux package, an implementation of a previously described method

to integrate gene-expression data in a continuous way into genome-scale metabolic network

reconstructions. We show, as an example, how the integration of a set of simulated data

modifies the behavior of the E.coli core metabolic model using Flux Balance Analysis

simulations. Also, an example of the measurement of flux change between metabolic

scenarios was shown.

fluxModel1 fluxModel2 foldChange ADK1 4.547474e-13 1.000444e-11 21 D_LACt2 -6.821210e-13 1.364242e-12 3 LDH_D -6.821210e-13 1.364242e-12 3

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